A substrate material can be separated into two or more pieces by forming a plurality of laser-induced channels along a process path located along an intended line of separation, as taught by Bareman et al. in U.S. Pat. No. 8,842,358. A laser-induced channel edge can be formed upon substrate separation and can have a relatively smooth surface without the need for post-processing operations such as grinding. The thickness of the substrate through which such laser-induced channels can be formed has been somewhat limited, as has the consistency of the laser-induced channels along the substrate thickness.